Spanish language learning forums - Why is it "Me voy a dormir" instead of

For the first question, you need to look at the construct in its infinitive form - ir a dormirse.
This construct is used to express what is going to happen.

Note that 'ir' is followed by 'a' in the construct. That will always be the case, so it must always appear after the conjugated form of 'ir'.
Contrary to what everybody seems to teach, the Spanish infinitive does not mean 'to ...'. That is one of the English translations, because English has both a full infinitive (with the 'to') and a bare infinitive (without the 'to'). Spanish has only a bare infinitive. So, when a preposition is necessary before the Spanish infinitive, it must be explicitly stated.
The second infinitive in the construct is a reflexive verb. That is why it has a suffixed reflexive pronoun - 'se'. The reflexive pronoun must agree in person with the subject. When the English subject is 'I', the English reflexive pronoun is 'myself'. In Spanish, the reflexive pronoun equivalent is 'me'.
Since the second infinitive in the construct is not conjugated (remains an infinitive), the person-appropriate pronoun may either remain suffixed to it or it may precede the conjugated verb in the construct.
So, 'me voy a dormir' and 'voy a dormirme' are equivalent constructs. Both mean "I'm going to fall asleep."

The second question has to do with one of the many uses of 'se'. In both of the constructs you questioned, the pronoun is an example of the impersonal 'se'. This is used when the subject is no one in particular.
'Se puede' can be translated a few different ways, but the American English 'you can' or 'they can', where neither subject is a particular individual or particular individuals, is the closest. The best translation of 'Sí, se puede' is 'Yes, one can', albeit this impersonal pronoun is falling out of usage in American English.

By the same token, 'Se habla español' can be translated 'One speaks Spanish'.

This last construct also has another translation, if context so directs, and is another example of how 'se' can be used.

Known as the 'pasiva refleja', using the pronoun 'se' is one of the ways to express the English passive voice in Spanish. (Spanish also has a 'voz pasiva' construct, but it is not used nearly as much as this passive 'se' construct.)
The English equivalent of 'se habla español' is 'Spanish is spoken (here)', which appears in the English passive voice, even though the Spanish passive voice was NOT used. Again, Spanish has two ways to express what we English speakers have to translate to the passive voice.

After all is said and done, I hope you've learned that a 'se' construct can have different translations into English, and there are other uses of the pronoun 'se', as you'll soon learn.

My advice is that you try not to rely on literal translations. That'll just impede your progress.
Just know that these 'se' constructs are used everyday in Spanish and have an everyday English equivalent. The literal translations will leave you wanting, to say the least. :)